Question

the venn diagram shows sets a, b, c, and the universal set u. shade (c ∪ a) ∩ b on the venn diagram.

Explanation:

Step1: Find the complement of C

The complement of set C, $C'$, is all the elements in the universal set U that are not in C. So shade the region outside of circle C.

Step2: Find the union of $C'$ and A

The union $C'\cup A$ is all the elements that are in $C'$ or in A or in both. So add the region of circle A to the already - shaded region of $C'$.

Step3: Find the intersection with B

The intersection $(C'\cup A)\cap B$ is all the elements that are in both $(C'\cup A)$ and B. So shade only the part of the shaded region from Step 2 that overlaps with circle B.

Answer:

Shade the part of circle B that overlaps with the region outside of circle C and circle A.